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Sunday, July 3, 2011

Complex Instruction

In her book What's Math Got to Do With It?, Jo Boaler wrote about 'complex instruction' as a vital part of making groupwork function effectively. What I read intrigued me, so I searched for more detailed information online, but I couldn't find much.

This past week I was able to attend a workshop on Complex Instruction put on by the Center for Innovative Teaching, at the Urban School in San Francisco. The workshop was led by Laura Evans, who did a fabulous job of introducing us to these powerful ideas. I'm going to try to explain what I got out of this two-day workshop, but my head is spinning, so I might miss vital pieces or misrepresent parts of the theory. If you were there, and saw different aspects, please speak up. I was the only college teacher there, but there were only a few things I had to translate for my situation.

Here's how it works: Start with a group-worthy task, make sure the students are ready in their groups, and understand the roles they're expected to play, give clear and detailed instructions about how they should work together and what to do when they think they've completed their task. Then, let the math-play (play and work are equivalent in a context like this, right?) begin!

A group-worthy task ...

is open-ended

is based on discovery

is challenging

requires multiple abilities

can be represented in more than one way

I'll feel like I really understand this when I can take a task/problem and evaluate it based on these criteria. I'm not there yet. I also need to be able to look at the curriculum we have and decide what sorts of group-worthy tasks would help the students learn each bit.

'Smart in Math'
Before students work in groups, it's important to help them understand that we typically have many misconceptions about what it means to be 'smart'. Typically, people think that someone who is 'smart in math' ...

answers questions quickly

always gets the right answer

doesn't have to work at it

But, really, people who are good at math ...

are persistent

wonder about relationships between numbers, shapes, functions, ...

check their answers for reasonableness

make connections

are willing to try things out, experiment, take risks

are resilient

want to know why

contribute to group intelligence by asking good questions

notice and learn from their mistakes

try to extend and generalize their results

Students may also need to know how synapses (the connections between neurons that are created each time you learn something new) are strengthened by repeated use. A new connection isn't strong until it's been used:

multiple times

in multiple ways

after a time away

Roles for Group Members
Before the groups dive into a math task, the group members also need to understand the roles they'll take on. Any teacher interested in using these ideas can modify these roles, but the idea is to give students plenty of coaching in how to work productively, and much less coaching on how to do the math.

The Facilitator asks if everyone understands what's been said, if anyone has a question, ...

The Team Captain keeps the group on task, reminds people of how they're supposed to proceed, makes sure everyone's ideas are heard.

The Resource Manager makes sure all conversations happen in the middle of the table, collects materials from the teacher, calls the teacher over when the whole group has a question, returns materials, ...

This list was part of the handout for the problem we were going to work on, which I'll describe next.

The Pile Pattern Problem

We needed to figure out the shapes for piles 5 and 6, and what their areas would be, and then to do the same for the 100th pile. We were also asked to think about the 1st and 0th shape, and if possible the -1th shape. While we worked on our mathematical task, Laura walked around and took notes on what we said to one another. She came up to us at an opportune moment and said things like, "Sue, it was really neat when you said 'I was thinking this, but it sounded like you were thinking about it this other way', you made connections between your thoughts and Rachel's." She had a very specific bit of praise for each of us, related to how we worked within the group, to solve the problem.

We all presented parts of our solutions to the whole group (of about 20). We were able to look at the pattern geometrically, algebraically, numerically, and graphically. We had a recursive formula for the area and an explicit one. We figured out what the 1st shape (#1) would have been, and hypothesized about the #0, #-1, and #-2 shapes. There were definitely some interesting twists to the problem.

Every step along the way, Laura would mention bits about how she'd do this with students. Make sure the group that only got one part gets to go first, have each group after that present one new way of looking at this problem.

Status
Within a group of high school students, each student has high or low social status and high or low academic status. (My question: How is this different among college students?) If someone is quiet, it's generally because they don't expect their group to be interested in what they have to say, either because of past experience or because of subtle cues from other group members. Laura said, "Students hesitate to share as a way to hide or protect their status. High or low status is a great barrier to risk taking."

The teacher's job is to change that dynamic in a few ways. She has already told the group very explicitly what each person can do to help. She can also look for ways to 'assign competence' to students who have low status. If a low social status student has asked a question, she might mention how that was a great risk to take, and how it helped the group. Laura again, "When we raise their status, we give students excuses to take the risk that they deep down want to take."

I loved this workshop, and I hope to be able to implement some of the ideas. I wish the workshop had been longer. It would have been great to have a chance to practice finding or creating a group-worthy task, writing up instructions for it, seeing how groups work through it, and responding to the 'students' by commenting on how they're working together instead of offering them math tips.

Edit on 5-30-13: When I wrote this, there were no complex instruction resources online. Now there is this website - it looks good.

I gave some thought to the "group-worthy" part of it, so maybe I can help there a bit:

A closed-ended task is problematic for groups, because the fastest person gets the answer and the experience is unrewarding (pedagogically and psychologically) for the rest. Two people with very closely matched styles and speeds can solve closed-ended problems together... occasionally - and this is hard to arrange and does not scale.

Likewise, direct teaching tasks (as opposed to discovery) are better done either individually ("go watch Khan videos, pause and rewind as needed") or in whole groups where questions of each person are answered for the benefit of the group. Besides discovery, group tasks can also be art, composition, construction or evaluation. They have to be about students creating/remixing/sharing, rather than "taking knowledge in."

A group is stronger than individuals, so mundane (non-challenging) tasks are a waste of this resource. Usually, mundane tasks lead to groups quietly falling apart and divvying the tasks for individual work, anyway.

Unless the group is completely homogeneous (think "attack of the clones"), tasks that require multiple approaches will allow different people to self-select for different roles and activities. Any challenging task will require multiple abilities, by the way, so the two requirements are redundant as far as problem selection goes. But they help us to understand situations.

Anything can be represented in more than one way, so I am not sure about this last requirement being significant.

@Sue I think specifically it's the group worthy tasks issue. I could devote all my time to trying to find/create these. I've got "Designing Group Work" as my resource. Was there anything else recommended?

For me, it's both finding groupworthy tasks and having the courage (and skill at bringing students along) to implement it.

For the groupworthy tasks, we need a good site that shows a traditional curriculum for each course, and gives good tasks to use that relate to each 'skill'. I plan to put out what I have so far, but it's not much.

I took a CI class in Seattle and couple years ago and loved it. Since then, I have found that it is challenging to come up with/find tasks that are truly group-worthy. When I do, however, CI works amazingly well.

The other thing about CI that is fun/challenging to learn/stretch/grow is status. Status is not on most teachers' radar (certainly not mine for the longest time), but once you're aware of it, and do things like "assigning competence" (I can't remember where I learned about that), I feel that it is really helpful to all kids--not just the low-status kids.

I love your post on CI. My credential program was heavy on developing CI in the classroom and I have found it to be hugely successful in helping students enjoy math and develop confidence in their mathematical ability. In particular, I like your discussion of the "habits" of someone who is good at math. I am trying to flush out a list of my own and would love your input. (http://www.doingmathematics.com/2/post/2012/02/habits-of-a-mathematician-take-one.html)

Also, here are a couple great resources if you haven't already seen them:

Your list looks fine. I was going to introduce you to Avery's work, but I see you've already linked to that.

I think each teacher's list will be different, depending on how the teacher works with students, and that's a fine thing.

Your list is way shorter than Avery's, and if I had a list, it might be shorter than yours. I don't have a list, but I often talk to students about 'making a simpler problem with the same structure', to give themselves more insight, my favorite advice from Polya.

Hi Katie, thanks for requesting the picture. I think I've fixed it. (Blogger seems to have deleted most (all?) of my pictures. I don't have the time to put them all back up at once, but I can put them back when people request.)